In a private meeting held hours before his prime-time address, President Obama was challenged by his 2008 presidential campaign rival Sen. John McCain.

Washington (CNN) – Hours before he was set to address the nation on his new Afghanistan strategy, President Obama and members of his war council spent about an hour briefing senior members of Congress at a White House meeting that multiple sources described as businesslike and sobering.

Democratic and Republican lawmakers, who attended the meeting, said Obama laid out his plans to escalate the military mission before several lawmakers asked questions.

Senate Majority Whip Dick Durbin told CNN the president emphasized that in addition to sending some 30,000 additional troops to Afghanistan, he also has a "target for when this is coming to an end."

"The president believes that gives the Afghans enough time, and the Pakistanis enough time to take control of the situation," Durbin said.

Three GOP sources told CNN that Sen. John McCain used the meeting to directly challenge the president on his exit strategy.

The sources said that Senate Minority Leader Mitch McConnell deferred to McCain, who questioned the concept of announcing now plans to begin withdrawing in July, 2011.

These sources said the president responded to McCain by promising that the withdrawal would be based on conditions on the ground.

House Majority Whip Jim Clyburn was one of the only members of the Democratic leadership in either chamber to tell CNN "I'm very supportive of it."

Even Durbin, one of the president's closest allies, told CNN he is withholding judgment. "The president took some time to reach his decision, I'm going to need some time to reach mine," Durbin said.